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Title: Analysis of algebraic flux correction schemes
Authors: Barrenechea, Gabriel R.John, VolkerKnobloch, Petr
Issue Date: 2015
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2107, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: A family of algebraic flux correction schemes for linear boundary value problems in any space dimension is studied. These methods main feature is that they limit the fluxes along each one of the edges of the triangulation, and we suppose that the limiters used are symmetric. For an abstract problem, the existence of a solution, existence and uniqueness of the solution of a linearized problem, and an a priori error estimate, are proved under rather general assumptions on the limiters. For a particular (but standard in practice) choice of the limiters, it is shown that a local discrete maximum principle holds. The theory developed for the abstract problem is applied to convection-diffusion-reaction equations, where in particular an error estimate is derived. Numerical studies show its sharpness.
Keywords: Algebraic flux correction method; linear boundary value problem; well-posedness; discrete maximum principle; convergence analysis; convection-diffusion-reaction equations
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik



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